Download Protein Data Condensation for Effective Quaternary Structure

Protein Data Condensation for Effective
Quaternary Structure Classification
Fabrizio Angiulli1 , Valeria Fionda2 , and Simona E. Rombo1
1
DEIS - Università della Calabria
Via P. Bucci 41C
87036 Rende (CS), Italy
{f.angiulli,simona.rombo}@deis.unical.it
2
Dept. of Mathematics
Via P. Bucci 31B
87036 Rende (CS), Italy
[email protected]
Abstract. Many proteins are composed of two or more subunits, each associated
with different polypeptide chains. The number and the arrangement of subunits
forming a protein are referred to as quaternary structure. The quaternary structure of a protein is important, since it characterizes the biological function of the
protein when it is involved in specific biological processes. Unfortunately, quaternary structures are not trivially deducible from protein amino acid sequences.
In this work, we propose a protein quaternary structure classification method exploiting the functional domain composition of proteins. It is based on a nearest
neighbor condensation technique in order to reduce both the portion of dataset
to be stored and the number of comparisons to carry out. Our approach seems to
be promising, in that it guarantees an high classification accuracy, even though it
does not require the entire dataset to be analyzed. Indeed, experimental evaluations show that the method here proposed selects a small dataset portion for the
classification (of the order of the 6.43%) and that it is very accurate (97.74%).
1 Introduction
Proteins are important components of the cell life, catalyzing most of the living cells reactions and controlling virtually all the cellular processes. Proteins are complex molecules composed by individual units called amino acids.
While an increasing number of amino acid sequences is produced and stored in
public databases, the geometric conformation of a protein can be determined by slow
and expensive methods (such as, for example, crystallography and NMR spectrometry).
Thus, a number of computational methods have been developed in the last few years to
predict and classify protein secondary, tertiary and quaternary structures [4, 10, 14, 15,
21]. In this paper, we focuses on protein quaternary structures. In particular, we deal
with the problem of efficiently exploiting available databases of amino acid sequences
in order to predict the number of subunits of a given protein.
In the rest of this section, we first recall basic concepts concerning protein structure
and then point out our contributions.
Background on protein structure. The sequence of the amino acids of a specific protein
is determined by the sequence of the bases in the gene encoding for that protein. Chemical properties of the amino acids composing a protein determine its biological activity.
Considering also the order in which amino acid residues lie in the chain, the amino acid
sequence is called primary structure of the protein. It is possible to univocally identify
a protein when the corresponding primary structure is known, but other information
about protein spatial conformation are necessary to have a complete description of its
biological functions. In particular, the secondary structure of a protein is represented
by the sequence of the repeated patterns of its backbone folding, without any regard
to the conformations of its sidechains; the most common secondary structure configurations are α-helix and β-strand [13]. The tertiary structure of a protein refers to the
three-dimensional structure of the entire polypeptide, specified by the coordinates of
each of its amino acids. Thus, both secondary and tertiary structures contribute to the
geometrical description of proteins. Actually, several proteins (e.g., Hemoglobin) are a
combination of two or more individual polypeptide chains. The arrangement according
to which such subunits assemble is called the protein quaternary structure. Quaternary
structure refers to the number of subunits involved in forming a protein, to their interconnections and to their organization [12, 17]. Biological processes are often influenced
by the quaternary structure of proteins involved therein; e.g., the subunit construction
of many enzymes provides the structural basis for the regulation of their activities. Proteins having a quaternary structure are called oligomers, and may be further classified as
homo-oligomers, consisting of identical subunits, and hetero-oligomers, made of subunits that are different from one another. Furthermore, based on the number of subunits
linked together, an homo-oligomer may be an homodimer, an homotrimer, an homotetramer, etc. Proteins consisting of only one subunit are called monomers.
Contributions. In this paper, we propose a classification method to individuate the number of subunits of each protein of a given dataset.
To this aim, we exploit protein functional domain information, as already successfully
done in previous literature [21]. We encode each protein by a vector whose elements are
associated to PFam domains [3]. The number of subunits included in a given protein is
then obtained by assigning that protein to a class (e.g., monomers, homodimers, etc.),
on the basis of a previously classified dataset and of a suitable classification method.
A few approaches have been recently introduced to support protein quaternary structure
classification [5, 10, 16, 21, 22]. The most successful of them [21, 22] reach at most the
87.5% of overall accuracy, and the maximum dataset size they considered is of about
10,000 proteins. Furthermore, most of the quaternary structure classification methods
proposed in the literature store and use the overall dataset, comparing each protein to
be classified to each stored protein. This may result hard when large datasets are to be
considered.
Our approach gives a contribution in the direction of reducing both the portion of dataset
that is necessary to store and, consequently, the number of comparisons to carry out at
classification time, allowing sensible space and time savings, while achieving very good
accuracy figures.
In particular, we exploit nearest neighbor condensation techniques (as the one recently
introduced in [1]) to replace the whole protein dataset with a notable subset that can be
then used for the sake of fast protein quaternary structure prediction. With this aim, we
use a training set consistent subset for the nearest neighbor decision rule as reference
dataset during classification. Let T be a dataset. Having fixed a meaningful distance
metrics, a subset S of T is a training set consistent subset of T for the nearest neighbor
rule, if S correctly classifies all the objects of T by means of the nearest neighbor rule.
To evaluate our method, we considered two different kind of tests. First, we performed
the 10-fold cross-validation on a very large protein dataset including 20,068 proteins
taken from the SWISSPROT [2] database. The results confirmed the effectiveness of our
approach. In fact, we scored an overall accuracy of 97.74%, by using only the 6.51% of
the total dataset. This result is important, since pinpoints that our method can be adopted
to correctly classify proteins whose quaternary structures are unknown, notably reducing the portion of dataset to analyze. Such a reduction is particularly attractive in the
case of protein quaternary structures classification, where large datasets are often to be
considered. The second kind of tests concerns the exploitation of the jackknife crossvalidation on a non-redundant dataset already used to test another successful technique
proposed in the literature [21]. Also in this case, the results we obtained show that our
method is more powerful than the previous ones, being able to obtain comparable accuracy in the classification of quaternary structures, even if using only the 45.39% of the
whole dataset.
The rest of the paper is organized as follows. Section 2 briefly surveys related work,
addresses differences with our approach, and precisely highlights contribution of this
work. Section 3 describes our protein quaternary structure classification method. Section 4 presents experimental results. Finally, Section 5 reports conclusions and future
work.
2 Related Work
Recently, some techniques have been proposed for protein quaternary structure classification [5, 10, 16, 21, 22]. Most of them aim at classifying homo-oligomeric proteins, by
storing and exploiting the overall considered dataset and comparing each protein to be
classified to each stored protein.
In [10] a software, called Quaternary Structure Explorer (QSE), is presented. The method
is based on the analysis of protein amino acid sequences to distinguish between homodimers and non-homodimers, by exploiting rule-based classifiers. The C4.5 machinelearning algorithm is used, and proteins are represented by 401 amino acid indices. The
overall classification accuracy of the approach is 70%.
The method proposed in [16] uses the function of degree of disagreement (FDOD),
that is, a measure of information discrepancy, to discriminate between homodimers and
other homooligomeric proteins by exploiting information on the primary structure of
proteins, enriched with subsequence distributions of such primary sequences to take
into account the effect of residue order on protein structure. The technique scores an
overal success rate of the 82.5%.
In [22] both the support vector machine (SVM) and the covariant discriminant algorithms are exploited to predict quaternary structure properties from the protein primary
sequences. The authors consider the amino acid composition and the autocorrelation
functions based on the amino acid index profile of the primary sequence, obtaining at
the best an accuracy equal to the 87.5%.
The techniques presented in [10, 16, 22] are able to distinguish just between two classes,
that are, homodimers and non-homodimers, whereas our approach is able to discriminate among any number of classes. In this respect, our method is more similar to the
two approaches illustrated in the following.
The main contribution of the work [5] is the exploitation of a pseudo amino acid composition to express a protein in terms of a set of discrete numbers, which is more powerful
than the standard amino acid composition. In fact, it is able to take into account a considerable amount of sequence-order effects. An overall success rate of 80.1% on a set
of 332 test proteins was obtained.
The four approaches described above exploit only protein sequence information, without any regard for protein domain composition. Our method is different, as we consider
the protein domain composition that, according also to other studies [19, 11, 6, 4, 20],
is able to deliver important information about protein structures and functions, which
may be related to protein quaternary structure composition.
The approach presented in [21] is based on the functional domain composition of proteins and on the nearest neighbor algorithm (NNA). They performed the jackknife crossvalidation test on a non-redundant dataset of 717 proteins, and then exploited the nonredundant dataset to classify an independent dataset of 9,951 proteins. They obtained,
resp., an overall success rate of 75.17% and 84.11% for the two dataset.
In our experiments, we used the same non-redundant dataset exploited in [21], enriched
in the number of considered domains, obtaining some accuracy improvements (see Section 4). Differently from [21], where a generalized distance (which is not a metric) has
been exploited in the classification method, we used the Jaccard distance as the distance
metric. Furthermore, our technique is more efficient than the one presented in [21] and,
in general, than the other related techniques, due to its ability of classifying proteins
without the necessity of making comparisons with all the elements of the dataset. Indeed, we are able to extract a relatively small subset of the training set to carry out such
a classification without any significant loose in precision.
To summarize, our approach is more general than previous methods, such as [10, 16,
22], that are specific for the classification of only two classes of protein quaternary
structures. Furthermore, we exploited the protein representation which is shown to be
the most complete in terms of protein functional information (i.e., functional domain
composition), and we achieve high accuracy values even if exploiting small dataset portions. All these features grant to our method highest overall success rate than the other
ones presented in the literature (97.74%), making it attractive especially when large
protein datasets are to be handled.
3 Classification method
Next, we describe the classification method to individuate the number of subunits of
each protein of a given dataset. In the following we will refer as PQSC-FCNN, for
Protein Quaternary Structure Classification through FCNN rule, to the classification
method here presented. In order to design an effective and efficient classification method,
different issues are to be addressed. Among them: the feature space and distance metrics to adopt, the classification algorithm, and the suitability of the overall method.
As already pointed out, most of the quaternary structure classification methods proposed in the literature, store and use the whole available dataset, comparing each pro-
tein to be classified to each stored protein. This may result hard when large datasets are
considered. Hence, we would like to drastically reduce the portion of the dataset that is
necessary to store and, consequently, the number of comparisons to carry out, allowing
sensible space and time savings.
To this end, we exploit protein functional domain information, and encode each protein by a binary vector whose elements are associated to PFam domains [3]. We adopt
the Jaccard metric as our distance measure and exploit the k nearest neighbor rule [7,
?,?], one of the most extensively used nonparametric classification algorithms, which
is simple to implement and yet powerful. The rationale underlying this choice is that
for this classification rule there exist efficient techniques to reduce both space and time
requirements, that we will use in order to reduce the already classified protein dataset.
In the following, the adopted protein representation, distance metrics, classification rule,
and data reduction method are detailed.
Protein representation. To characterize proteins, we adopted the functional domain
composition, since this kind of representation has been proved to be successful both for
the specific problem we analyzed [21], and for the solution of other related problems,
such as the prediction of protein-protein interactions [19, 11], of protein structures [6]
and of protein functions [4, 20]. Protein functional domains are elements of the protein
structure that are self-stabilizing and often fold independently of the rest of the protein
chain. According to the functional domain composition, a protein is represented by a
binary vector with size equal to the number of exploited domains. In particular, let D
be an ordered set of protein domains, which have been considered to characterize the
proteins in a dataset P . Then, each protein p ∈ P is represented by a vector vp of |D|
elements. The element vp [i] is set to be one if p contains the i-th domain in D, zero
otherwise.
Distance metrics. We used the Jaccard metric as our distance metric, which is very
suitable for binary data. In particular, the Jaccard distance between two protein vectors
vp1 and vp2 is defined as:
n2 + n3
d(vp1 , vp2 ) =
n1 + n2 + n3
where n1 is the number of indexes for which the correspondent elements are equal to
one in both vectors, n2 is the number of indexes for which the correspondent elements
are equal to one in vp1 and to zero in vp2 , n3 is the number of indexes for which the
correspondent elements are equal to zero in vp1 and to one in vp2 .
Classification rule. The nearest neighbor rule [7] is widely used as a classification algorithm. It is simple to implement and yet powerful, due to its theoretical properties
guaranteeing that for all distributions its probability of error is bounded above by twice
the Bayes probability of error. The nearest neighbor decision rule can be generalized
to the case in which the k nearest neighbors are taken into account. In such a case, a
new object is assigned to the class with the most members present among the k nearest
neighbors of the object in the training set. This rule has the additional property that it
provides a good estimate of the Bayes error and that its probability of error asymptotically approaches the Bayes error [9].
The naive implementation of the NN rule has no learning phase, since it requires to
store all the previously classified data, and then to compare each sample point to be
classified to each stored point. In order to reduce both space and time requirements,
several techniques to reduce the size of the stored data for the NN rule have been proposed (see [18] for a survey). In particular, among those techniques, the training set
consistent ones, aim at selecting a subset of the training set that correctly classifies the
remaining data through the NN rule.
Data reduction. In order to reduce the reference protein quaternary structure dataset
used during classification, we exploited the Fast Condensed Nearest Neighbor rule [1],
FCNN for short, an algorithm computing a training set consistent subset for the NN
rule. Informally, having fixed a meaningful distance metrics and a dataset T , a subset S
of T is a training set consistent subset of T for the nearest neighbor rule, if S correctly
classifies all the objects of T by means of the nearest neighbor rule. Thus, loosely
speaking, the objects of the subset S can be regarded as representing the objects of T
which are not in S, and training set consistent subset methods for the nearest neighbor
rule can be regarded as methods to filter out dataset instances which can be considered
unessential to correctly classify new incoming objects.
The method is recalled next. We provide some definitions first. We define T as a labelled
training set from a metric space with distance metrics d. Let x be an element of T . Then
we denote by nnk (x, T ) the kth nearest neighbor of x in T , and by nnsk (x, T ) the set
{nni (x, T ) | 1 ≤ i ≤ k}. l(x) will be the label associated to x. Given a point y, the
k-NN rule NNk (y, T ) assigns to y the label of the class with the most members present
in nnsk (y, T ). A subset S of T is said to be a k-training set consistent subset of T if,
for each y ∈ (T −S), l(y) = NNk (y, S). Let S be a subset of T , and let y be an element
of S. By V or(y, S, T ) we denote the set {x ∈ T | ∀y 0 ∈ S, d(y, x) ≤ d(y 0 , x)}, that
is the set of the elements of T that are closer to y than to any other element y 0 of S,
called the Voronoi cell of y in T w.r.t. S. Furthermore, by V oren(y, S, T ) we denote
the set {x ∈ (V or(y, S, T ) − {y}) | l(x) 6= NNk (x, S)}, whose elements are called
Voronoi enemies of y in T w.r.t. S. Centroids(T ) is the set containing the centroids
of each class label in T . The FCNN rule relies on the following property: a set S is a
training set consistent subset of T for the nearest neighbor rule if for each element y of
S, V oren(y, S, T ) is empty.
The FCNN algorithm initializes the consistent subset S with a seed element from each
class label of the training set T . In particular, the seeds employed are the centroids of the
classes in T . The algorithm is incremental. During each iteration the set S is augmented
until the stop condition, given by the property above, is reached. For each element of
S, a representative element of V oren(y, S, T ) w.r.t. y is selected and inserted into S.
Such a representative element it is the nearest neighbor of y in V oren(y, S, T ), that is,
the element nn(y, V oren(y, S, T )) of T .
As for the time complexity of the method, let N denote the size of the training set T
and let n denote the size of the computed consistent subset S. Then the FCNN rule
requires N n distance computations to compare the elements of T with the elements of
S. However, if the distance employed is a metric, a technique exploiting the triangle
inequality further reduces this worst case computational cost [1].
4 Experiments
In this section, we illustrate the experimental evaluation of the method proposed in this
paper. To build our datasets, we downloaded proteins from the SWISSPROT database
Large dataset
Classes
PQSC-FCNN, k = 2
Corr/Tot % Accuracy
Monomer
6,114/6,184 99.45%
Homodimer
8,408/8,690 96.75%
Homotrimer
1,154/1,190 96.97%
Homotetramer
2,422/2,513 96.38%
Homopentamer
232/237
97.89%
Homohexamer
759/784
96.81%
Homoheptamer
4/5
80.00%
Homooctamer
457/465
98.28%
Overall
97.60%
% Dataset Exploitation
6.43%
PQSC-FCNN, k = 3
Corr/Tot % Accuracy
6,130/6,184 99.13%
8,427/8,690 96.97%
1,150/1,190 96.64%
2,452/2,513 97.57%
232/237
97.89%
761/784
97.07%
4/5
80.00%
458/465
98.49%
97.74%
6.51%
PQSC-FCNN, k = 4
Corr/Tot % Accuracy
6,135/6,184 99.21%
8,402/8,690 96.68%
1,136/1,190 95.46%
2,380/2,513 94.71%
232/237
97.89%
742/784
94.64%
4/5
80.00%
458/465
98.49%
97.11%
6.70%
Table 1. Overall success rate obtained by the 2-FCNN, the 3-FCNN, the 4-FCNN methods on a
dataset of 20,068 proteins.
[2], available at www.ebi.ac.uk/swissprot/, and domains from the PFam database
[3], available at http://www.sanger.ac.uk/Software/Pfam/.
We considered two different experiments. The first experiment consisted in running the
10-fold cross-validation on a very large protein dataset consisting of 20,068 proteins.
The number of considered domains is 1,816. The results of this experiment are shown
in Table 1. The first column of the table contains the homo-oligomeric class names,
the second, third and fourth ones report both the number of correctly predicted proteins w.r.t. their total number and the percentage of accuracy scored by PQSC-FCNN
for k = 2, k = 3 and k = 4, respectively, for each class. In the last two rows of the
table, the overall accuracy and the percentage of exploited dataset are reported. The results confirmed the effectiveness of our approach. In fact, the maximum overall success
rate obtained on the entire dataset is of the 97.74%, and the minimum dataset exploitation is drastically reduced to the 6.43% of the original dataset. In general, as for the
classification accuracy the three values of k were comparable, being equivalent on the
homopentamers and on the homoheptamers, while only for k = 3 and for k = 4 the
method returns the same results for homooctamers.
Table 2 shows detailed information about the condensed set generated by the method
on the overall dataset of 20,068 proteins. In particular, for each class, both the number
of elements of the condensed set belonging to that class, and the reduction percentage
w.r.t. the total number of elements in that class, are reported. The number of elements
and the reduction percentage of the overall condensed set are shown on the last row of
the table. By using these three values of k, the method extracted condensed sets with
the same size per class for homopentamers, homoheptamers and homooctamers. For
the homoheptamer class, the reduction percentage is notably higher than for the other
classes, due to the few elements belonging to that class (only 5 ones). The reduction
percentage on the overall dataset is 6.01% for k = 2, 6.10% for k = 3 and 6.32% for
k = 4. This show the power of the method, as it is sufficient to explore only a bit more
than the 6% of the overall dataset to (most probably) classify a new protein.
Both the exploited protein datasets and the correspondent domains can be downloaded
at the web-links reported in Section 5.
Condensed set
Classes
PQSC-FCNN, k = 2
PQSC-FCNN, k = 3
PQSC-FCNN, k = 4
Number of elements Percentage Number of elements Percentage Number of elements Percentage
Monomer
98/6,184
1.58%
153/6,184
2.47%
157/6,184
2.54%
Homodimer
643/8,690
7.40%
649/8,690
7.47%
718/8,690
8.26%
Homotrimer
145/1,190
12.18%
101/1,190
8.49%
108/1,190
9.08%
Homotetramer
197/2,513
7.84%
199/2,513
7.92%
157/2,513
6.25%
Homopentamer
17/237
7.17%
17/237
7.17%
17/237
7.17%
Homohexamer
74/784
9.44%
74/784
9.44%
79/784
10.08%
Homoheptamer
3/5
60.00%
3/5
60.00%
3/5
60.00%
Homooctamer
29/465
6.24%
29/465
6.24%
29/465
6.24%
Overall
1, 206
6, 01%
1, 225
6.10%
1, 268
6.32%
Table 2. Condensed sets detailed information for the dataset of 20,068 proteins.
In order to compare our method with a related one, in the second kind of experiments
we considered the non-redundant protein dataset discussed by Yu et al. in [21]. The
main goal of this comparison is to show that our method may have accuracy comparable to those of related methods, while sensibly reducing the amount of labeled data
to exploit during classification. In particular, we point out that the method presented in
[21] utilizes a non redundant version of the overall protein dataset in order to cope with
problems associated with management of large data sets. As we will show in the following, our method will be able to halve even this non redundant dataset, while maintaining
the same accuracy as the competitor method.
Yu et al. adopted an approach based on the functional domain composition and employed the nearest neighbor algorithm (NNA) to classify protein quaternary structures.
They represented the 717 considered proteins by 540 domains. Here, we enlarge the
number of considered domains to 1,253 in order to obtain a more accurate representation of data. Thus, we compare PQSC-FCNN with NNA by running the jackknife
cross-validation on the non-redundant dataset, by considering the same 1,253 domains
representation for all methods.
We run PQSC-FCNN exploiting the Jaccard metric, whereas NNA has been run with
the generalized distance exploited in [21]. The results are illustrated in Table 3. The
first column of the table contains the homo-oligomeric classes, the second, third, fourth
and fifth ones illustrate both the number of correctly predicted objects w.r.t. the total
number of them and the percentage of accuracy scored by PQSC-FCNN for k = 2, for
k = 3 and for k = 4, and NNA, respectively, for each considered class. In the last two
rows of the table, the overall accuracy and the percentage of exploited dataset for each
method are reported. We can observe that all the considered techniques return the same
results for the two classes of homopentamers and homooctamers. The only class for
which PQSC-FCNN does not obtain higher accuracy than the NNA is the homodimer
class. However, for k = 4 it obtains a success rate of 78.51% for that class, w.r.t. the
80.00% scored by the NNA, and thus, also in this case, the two methods achieve comparable results.
For the homotrimer and the homotetramer classes, the PQSC-FCNN for k = 2 and the
NNA have the same accuracy scores, whereas in the remaining cases (i.e., monomers
and homoexamers), PQSC-FCNN always scores better accuracy than NNA, also with
Non-redundant dataset
Classes
PQSC-FCNN, k = 2
Corr/Tot % Accuracy
Monomer
177/208 85.10%
Homodimer
250/335 74.63%
Homotrimer
28/40
70.00%
Homotetramer
53/95
55.79%
Homopentamer
11/11
100.00%
Homohexamer
9/23
39.13%
Homooctamer
2/5
40.00%
Overall accuracy
73.92%
% Dataset
46.79%
Exploitation
PQSC-FCNN, k = 3
Corr/Tot % Accuracy
174/208 83.65%
250/335 74.63%
27/40
67.50%
52/95
54.74%
11/11
100.00%
9/23
39.13%
2/5
40.00%
73.22%
47.35%
PQSC-FCNN, k = 4
NNA
Corr/Tot % Accuracy Corr/Tot % Accuracy
178/208 85.58%
168/208 80.77%
263/335 78.51%
268/335 80.00%
27/40
67.50%
28/40
70.00%
42/95
44.21%
53/95
55.79%
11/11
100.00%
11/11
100.00%
10/23
43.48%
7/23
30.43%
2/5
40.00%
2/5
40.00%
74.34%
74.90%
45.39%
100%
Table 3. Comparison of overall success rate obtained by PQSC-FCNN and NNA.
some sensible improvements. In particular, for k = 4, PQSC-FCNN scores the accuracy value of 85.58% for monomers, which is about 4.81% higher than the success rate
obtained by the NNA, whereas it scores the accuracy value of 43.48% for homohexamers, which is about 13.05% higher than the success rate obtained by the NNA for the
same class and represents the best accuracy improvement w.r.t. NNA we obtained.
These results are significant since, for monomers and homoexamers, our method has
been able to obtain more accurate results than NNA even exploiting only the 45.39% of
the overall dataset, whereas [21] did not make any dataset reduction.
Summarizing, the PQSC-FCNN method is able to reach an overall success rate that
is greater than the NNA, even if it exploits only the 45.39 − 47.35% of the original
dataset. This means that PQSC-FCNN is more efficient than the method [21], allowing
both time and space savings without any significant loss in accuracy but, rather, often
allowing success rate improvements.
5 Concluding Remarks
We proposed a classification method for protein quaternary structures, by exploiting
protein functional domain information and FCNN rule. Experimental evaluations showed that our approach is able to reduce both the portion of protein dataset that is necessary
to store and the number of comparisons to carry out, allowing sensible space and time
savings even if guaranteeing high values of accuracy. Thus, the method is competitive
w.r.t. other methods presented in the literature. We illustrated some tests we carried out
on homo-oligomeric proteins, confirming the validity of our approach. Future efforts
will be devoted to investigate the problem of quaternary structure prediction for heterooligomers.
Additional material. The protein datasets we exploited are available on-line. In particular, the non-redundant dataset of 717 proteins is listed at:
http://siloe.deis.unical.it/PQSC FCNN/non redundant dataset.pdf,
together with the corresponding 1,253 domains we exploited for the functional domain
composition, while the 20,068 proteins of the second dataset and their 1,816 are available at:
http://siloe.deis.unical.it/PQSC FCNN/20068 dataset.pdf.
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